Question: Solve for $x$. Enter the solutions from least to greatest. $(x +1)(3x +4)=0$ $\text{lesser }x = $
Solution: For any two expressions $A$ and $B$ : If $A\cdot B=0$ then either $A=0$ or $B=0$. This is called the zero product property. In our case, $(x +1)(3x +4)=0$. So either $(x +1)=0$ or $(3x +4)=0$ : $\begin{aligned} (1)&&x +1&=0 \\\\ &&x&=-1 \end{aligned}$ $\begin{aligned} (2)&&3x +4&=0 \\\\ &&3x &= -4 \\\\ &&x&=-\dfrac{4}{3} \end{aligned}$ In conclusion, $\begin{aligned} \text{lesser }x &= -\dfrac{4}{3} \\\\ \text{greater } x &= -1 \end{aligned}$